Problem: What do the following two equations represent? $-3x+4y = -2$ $15x-20y = 5$
Explanation: Putting the first equation in $y = mx + b$ form gives: $-3x+4y = -2$ $4y = 3x-2$ $y = \dfrac{3}{4}x - \dfrac{1}{2}$ Putting the second equation in $y = mx + b$ form gives: $15x-20y = 5$ $-20y = -15x+5$ $y = \dfrac{3}{4}x - \dfrac{1}{4}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.